# 3.3 Waterfalls for Capital Returns

#### Introduction

As mentioned in the last section, in private equity deals, the GP (project Sponsor and Organiser) will take a higher share of the profits if the project is highly profitable, and a lower share for lower levels of profitability. The example of a profit share shown in the last section was based on distributing the absolute (\$ amount) of profit in each year according to some percentages for each party, where the size of each band was also determined in absolute (\$ amount) figures.

In practice, the size of the bands which determine the share split to apply (i.e. to split profits between the GP and LPs) is related to the amount of \$ capital (equity) and a return requirement or expectation. Thus, the bands are calculated in each period based on the (notional) capital present at the beginning of the period, given a return assumption. The principles behind the formulas to calculate the split of the cash payout in each period are the same as discussed earlier. The additional complexity is that the size of the bands changes each period, as the upper limit for each band is determined by adding:

• The capital balance at the start of the period.
• The return hurdle (applied to the starting capital balance).
• Any new capital injections made in the period.
Once the upper limit to the payout in the band is established, the payout is made up to this amount as long as sufficient cash flow is available. (Otherwise payment is made only up to the amount of available cash flow). Then, the ending balance for the capital is calculated, and this is brought forward to the next period.

#### Corkscrew Options

In order to implement the above calculations, it is most convenient to use a corkscrew-type structure, since there is an ending capital amount that needs to be brought forward for use as a starting amount.

The elements of the corkscrew in any period, and for each band, are

• Starting capital.
• The return hurdle.
• Capital injections.
• The upper limit for distributions within this band (i.e. sum of the above three elements).
• The actual amount of distributions witin the band (i.e. after considering the cash flow in the period).
• The remaining amount (if any) of cash flow, for distribution in higher bands.
• The ending capital balance for this band.
The corkscrew can be structurally built either by:
• For each corkscrew items, listing all the bands.

or:

• For each band, listing all the corkscrew items.

The first of these is shown in the image below; it corresponds to the structures in the previous section: In the second method, each band contains a corkscrew such as: This second method is used more frequently that the first (when a corkscrew calculation is required), as it is more compact: The single structure (for any band) contains all the logic required, and the structure can simply be copied to create an additional band.

The following provides a full worked example.

#### Example: Three Hurdle Capital-Returns Waterfall

For simplicity of presentation in this example, the distribution (payout) figures are shown as positive values (as in the green-shaded cells in the images). In some cases, modellers prefer to use negative values for cash distributions (in which case some formulas require the reverse signs to be used in the appropriate formulas).

The following shows the cash flow profile of a six-year deal (including the first capital injection at the end of year 0), as well as the calculations for a first ban (in which the return hurdle is assumed to be 8% p.a.): For addition clarity, the formulas within the corkscrew are shown again here: Note that by changing the return hurdle to 12%, one would simply increase the upper limit of the band (and reduce the amount that is above the band limit): In practice, one can therefore copy the structure for as many times as necessary (i.e. one structure for each hurdle rate target), to give (in the case of three hurdle targets or bands): Note that (for each band) the green-shaded cells represent the total distributions that are either below that band limit, or above that band limit. For example, for the second band, row 22 shows the total distributions in band 1 and band 2, whilst row 23 shows that total that is in band 3 or above. Therefore, to calculate the amount within each band, one must:

• For Band 1, it is the calculations of distributions up to the limit within Band 1 (i.e. row 13).
• For Band 2 it is the difference between the limits of Band 2 and Band 1 (i.e. row 22 less row 13).
• For Band 3 it is the difference between the limits of Band 3 and Band 3 (i.e. row 31 less row 22).
• For “above Band3”, it is item for “Total Distributions above upper Band Limit” for Band 3 (i.e. row 32).
A summary table of distributions by band is then: (The formulas highlighted in blue are for the first and last bands [which are direct cell references], whereas those with the red marking are for the interior bands [where the difference between items need to be calculated]).

Note that once the split by band is complete, the calculation for the amount due to GP and LPs is performed by multiplication with the relevant percentages (for the profit split in each band). It is not shown here as it was demonstrated in the last section, and is in any case very simple.

#### Further Illustration

It can be useful to illustrate the behaviour of this band structure with other examples.

First, if we take a project with a one-year horizon, consisting of an investment of \$100m, followed by a payout one year later of \$107m, then all of the \$107m is in the first band, since the return is 7% p.a. (i.e. less than the 8% required within Band 1): If the payout were instead \$108.5m (so that the return is 8.5% p.a.) then there would be \$0.5m in Band 2: If we consider a profile in which the payout exactly equals the return target for several years (i.e. a payout of \$8m per year), then the capital base is constant, so that all of these payouts fall into Band 1: Finally, if a payout is sufficient to have fully paid back the capital at the return target for Band 1, then all future payouts will be in Band 2 (and similarly for higher bands). In the following, the payout in year 3 is sufficient to to clear Band 1, and the payments in year 4 and 5 then clear Band 2, so that the payout in year 6 is all in Band 3: 